1. Technological Field
This invention relates to a method for estimating molecule concentrations in a sampling, and the equipment therefor.
2. Description of Related Art
Some apparatuses enable to separate the detection of different molecules in a sample along a signal that is a spectrum. The detected components typically appear as peaks whose height depends on the concentration of the molecule concerned in the sample. The liquid phase chromatographs and the mass spectrometers have this property by separating the molecules from their retention time in the column and their mass divided by the charge respectively. The apparatuses can be used together, and the resulting signal is then a multiple spectrum, showing a peak scattering on a plane as a function of the two parameters.
The measurements can be difficult to exploit because of the high number of molecules present in the sample and of the existence of isotopes that change the mass of some measured molecules with respect to their usual value and modify the peak shapes to give isotopic ranges that are less recognizable and less easy to measure. Another difficulty arises for elements that are present in a very low concentration and yet whose detection is sometimes necessary. The conventional signal analyses can then fail.
A conventional method consists thus in inferring a concentration of a molecule from the height or the area of its peak on the signal.
Another method consists of analysing the whole signal by a spectral analysis by making comparisons with a library of known spectra.
It is understood that these methods can result in insufficient results for peaks that are weakly marked by low concentration molecules, because of the noise of the signal or of the superimposing with surrounding peaks.
Other methods are based on probabilistic estimations including in particular Bayesian analyses. The mathematical problem y=Hx+b, where y refers to the measurements, H an inversion matrix, x the result to be found (magnitudes to be assessed) and b the noise, is solved in Kang, Preuss, Schwarz-Selinger and Dose paper, entitled “Decomposition of multicomponent mass spectra using Bayesian probability theory” (published in Journal of mass spectrometry, volume 37, July 2002, pages 748, 754), by assessing the noise as a Gaussian function of zero average and determined variance which results in an expression of the magnitudes of vector x in the form of a probability distribution. Moussaoui, Brie, Moahammed-DJafari, Carteret paper “Separation of Non-Negative Mixture of Non-Negative Sources Using a Bayesian Approach and MCMC Sampling” (published in IEEE transactions on signal processing, volume 54, November 2006, pages 4133 to 4145), and Mohammad-Djafari and al. paper “Regularization, maximum entropy and probabilistic methods in mass spectrometry data processing problems” (published in International Journal of mass spectrometry, volume 215, number 1 to 3, 1 Apr. 2002, pages 175 to 193), describe generalizations in which the coefficients of the matrix H are also considered as uncertain and modelled by different probability distributions. Such methods lead to numerous calculations since the number of coefficients is typically equal to the number of measurement points on the signal multiplied by the number of magnitudes to be assessed. Allocating a priori probability distributions to each of the coefficients of the matrix is arbitrary and can lead to results that are not very representative. Further constraints should generally be introduced to be able to solve the problem, however the data necessary to properly and accurately introduce them are often missing. As a result, these prior art methods do not ensure a suitable result despite of their will to express their results as the more realistic form of the probability distributions.